Gabriel Ribeiro Email: gribeiro@ethz.ch Expository notes Analog photography

I am a postdoctoral researcher at ETH Zürich working with Emmanuel Kowalski. My research lies at the interface of algebraic geometry and number theory, with a focus on étale and de Rham cohomology and their applications to character sums in analytic number theory. I am also interested in bringing tools from homotopy theory into these questions.

Publications & Preprints (arXiv)

Algebraic Geometry & Number Theory

• A moduli space of character sheaves. (arXiv version, 2026)

  In this paper, I study character sheaves on a commutative connected algebraic group \(G\): line bundles with flat connection \((\mathscr L,\nabla)\) satisfying a multiplicativity isomorphism \(m^*(\mathscr L,\nabla) \simeq (\mathscr L,\nabla) \boxtimes (\mathscr L,\nabla)\), where \(m\colon G\times G\to G\) is the group law. I construct a group algebraic space \(G^\flat\) whose points parametrize such character sheaves, and analyze its geometry. The main technical ingredient is a study of extension sheaves on the de Rham space \(G_\text{dR}\). An appendix provides self-contained, elementary proofs of basic results on de Rham spaces that may be of independent interest.

• Extensions of abelian schemes and the additive group. (arXiv version, 2025, joint with Zev Rosengarten)

  In this paper, we compute extension sheaves of abelian schemes and of the additive group by the multiplicative group in the fppf topology. Our main results include a generalized and streamlined proof of the Barsotti–Weil formula, the vanishing of \(\underline{\operatorname{Ext}}^2(A,\mathbb{G}_m)\) for an abelian scheme \(A\) over a general base, and a description of \(\underline{\operatorname{Ext}}^1(\mathbb{G}_a,\mathbb{G}_m)\) in characteristic zero.

Other

• IMProofBench: Benchmarking AI on Research-Level Mathematical Proof Generation. (arXiv version, 2025, joint with Johannes Schmitt et al.)

  I contributed research-level problems to IMProofBench, a private benchmark of 39 peer-reviewed proof tasks, each paired with automatically gradable subquestions. It evaluates tool-augmented LLMs in a workflow closer to real research (e.g. literature search and computer algebra), finding that models handle some accessible problems but still struggle on the hardest ones; Grok-4 leads on final-answer subquestions (52% accuracy), while GPT-5 is strongest on giving complete proofs (22% fully correct).

• Análise de nanocompósitos de polietileno de ultra alto peso molecular com carbeto de boro. (Published version, 2017, joint with Édio Junior et al.)

  In this article, written during my undergraduate studies, we investigated the incorporation of boron carbide into polyethylene nanocomposites with the aim of developing lighter and more resistant materials for the manufacture of bulletproof vests for the Brazilian Army.